Leapfrog for optimal control

C.Y. Kaya, Lyle Noakes

    Research output: Contribution to journalArticlepeer-review

    13 Citations (Scopus)


    The leapfrog algorithm, so called because of its geometric nature, for solving a class of optimal control problems is proposed. Initially a feasible trajectory is given and subdivided into smaller pieces. In each subdivision, with the assumption that local optimal controls can easily be calculated, a piecewise-optimal trajectory is obtained. Then the junctions of these smaller pieces of optimal control trajectories are updated through a scheme of midpoint maps. Under some broad assumptions the sequence of trajectories is shown to converge to a trajectory that satisfies the maximum principle. The main advantages of the leapfrog algorithm are that (i) it does not need an initial guess for the costates and (ii) the piecewise-optimal trajectory generated in each iteration is feasible. These are illustrated through a numerical implementation of leapfrog on a problem involving the van der Pol system.
    Original languageEnglish
    Pages (from-to)2795-2817
    JournalSIAM Journal on Numerical Analysis
    Issue number6
    Publication statusPublished - 2008


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